# Standard (mathematics)

From Citizendium, the Citizens' Compendium

*This article is about*

**the standard in mathematics**. For other uses of the term**standard**, please see standard (disambiguation).In mathematics, the word **standard** is often used in its non-technical sense
to indicate the "normally" or "most frequently" used of several options.
Words with a similar, but usually more formal and more technical meaning are:
normal, natural, canonical.
Thus there may be, for instance,

- a "standard" symbol that is usually (but not necessarily always) used, or
- a "standard" way to write an equation that need not be considered as a normal form.

Some very common examples for the use of the word "standard" are:

- The standard basis in
*d*-dimensional real or complex vector spaces (or, more generally, in any*d*-dimensional vector space*K*^{d}over a field*K*)

- is the basis formed by the
*d**d*-tuples

- In set theory,
*standard model*of the natural numbers usually refers to the set constructed inductively from the empty set.

- The term
*standard*(natural, real, complex, etc.)*numbers*is used to distinguish the usually used numbers from their nonstandard counterparts.

- In statistics the standard deviation is the most commonly used measure of variation.

- In mathematical physics there is a well-known standard model of particle physics.